Bend-twist Coupling Research Articles

Study on mechanical properties of wind turbine blades with bend-twist coupling effect

Bend-twist coupling (BTC), a method of passive load alleviation for turbine blade, has a significant influence on blade mechanical properties. The coupling behavior between bending and twisting motions stems from the material anisotropy in blade laminate or from the unique blade geometry such as sweep, deflection, and pre-bending. The material-based approach is employed in this research to determine influence regularity of BTC design on blade mechanical properties. To begin with, the blade property analysis tool PreComp that integrates a shear flow method with the classical laminate theory is adopted to compute the cross-sectional stiffnesses of the blades with different degree of BTC effect. Next, the bend-twist coupling coefficients for the BTC blades with different fiber orientation are calculated. Finally, the remaining mechanical properties including static performance, modal characteristics and buckling limits for different BTC blades are determined by the finite element method and the influence of changes in the degree of BTC effect on all these mechanical properties is further evaluated. The results show that the BTC effect markedly influences the different mechanical properties of the blade in different patterns. The 20° BTC blade has the highest BTC coefficient and the edgewise BTC coefficient at 100 m is 2.5 times higher than the flapwise BTC coefficient, while the maximum value of the torsional modal frequency of 3.8429 Hz and the greatest critical buckling load of 4328.1 kN corresponds to the 10° BTC blade and the 15° BTC blade respectively.

Harnessing fiber induced anisotropy in design and fabrication of soft actuator with simultaneous bending and twisting actuations

Most of the soft dielectric elastomer actuators (DEAs) are able to provide either planar or twisting deformations only. Development of a bio-inspired actuator with functionalities similar to the mammalian tongue or octopus tentacles is highly desirable for soft robotics applications. Here, design and fabrication of a multi-layered soft DEA capable of simultaneous bending and twisting actuation is reported through a unified computational and experimental approach. An anisotropic layer is introduced to couple the bending and twisting deformation in the conventional DEA. The fiber spacing and fiber orientation in the anisotropic layer is optimized with classical laminate theory (CLT) and finite element (FE) analysis. A multi-layered DEA with bending-twisting actuation is experimentally fabricated as a ‘proof of concept’. The computational and experimental results suggest that bend-twist coupling in multi-layered DEA can be suitably designed by varying the fiber spacing and orientation in the anisotropic layer. The twisting actuation of DEA enhances at the expense of bending deformation with an increase in the fiber angle. Finally, it is shown that a single anisotropic layer having 2 mm fiber spacing and 45° fiber orientation induces sufficiently large bending and twisting actuations in DEA. The findings of the present study will be a significant step ahead to develop bio-mimicking anisotropic actuators and grippers for soft robotics applications.

Solution of coupled mechanical behavior of bending-twisting coupled box structure based on multi-coupled laminates

The coupled mechanical behavior of composite bending-twisting coupled structure has still not been solved completely and effectively. In this paper, the analytical stiffness equation is derived for the bending-twisting coupled box structure with web, including the box structure composed of extension-shearing coupled laminate and the box structure composed of multi-coupled laminates. By combining deep learning with analytical derivation, the problem of accuracy deviation of analytical model introduced by boundary conditions is skillfully solved, and then the high-precision analytical solution of torsional deformation of box structure is realized. Based on the analytical model, the optimal design of the box structure is further realized. The results show that compared with the box structure composed of extension-shearing coupled laminate, the box structure designed by the multi-coupled laminates is able to reach higher bending-twisting coupling (up to 80%). Finally, the robustness of the couplings of laminates and box structures are analyzed respectively, and the hygrothermal stability and couplings of the box structure are verified by numerical simulation.

A lumped-parameter coupled electro-piezo-aeroelastic model for flapping wings

Induced-strain actuated flapping wings and fins, achieved by surface-mounted piezoelectric actuators, do not need conventional motors and mechanisms, potentially reducing system weight, energy consumption, and mechanical complexity compared to conventional systems. A piezocomposite flapping wing or an underwater oscillating fin with induced-strain actuation can interact with the ambient fluid to yield flow vectoring, control, and lift or thrust generation. In this article, an electro-piezo-aeroelastic coupled lumped-parameter model is developed to predict the dynamic behavior of strain actuated flapping wings, and obtain insight into coupling mechanisms such as bend-twist coupling, fluid-structure interaction, and electro-piezo coupling. The piezoelectric wing is modeled as a laminated orthotropic plate. Using the Rayleigh-Ritz method, the distributed wing motion can be represented by lumped wing heave, chordwise curvature, and pitch displacements by assuming prescribed deformation shapes. The assumed shapes are compatible with the fluid effects interpreted as translational and torsional added mass and damping to the structure. The aeroelastic model is then coupled to the circuit model via electro-piezo coupling. The mechanical model is validated using the finite element method. It is found that four wing tip parameters, including first and second order heave motion, pitch, and chordwise curvature are sufficient to represent the wing motion. The lumped parameter wing model is then used to investigate the system optimal parameters for maximizing desired aero- and/or hydro-dynamic responses. System properties such as structural parameters, excitation frequency ratio, etc., are under investigation. The lumped parameter model is computationally efficient, and suitable for trade studies and multi-disciplinary design optimization. Also, the lumped parameter model serves as a foundation for flapping flight analysis, e.g., analyzing lift force, leading-edge vortex stabilization, and tip vortex shedding.

A reduced-order multi-body model with electromechanical-aeroelastic coupling for mechanism-free ornithopters

Piezoelectric material-actuated so-called solid-state (i.e., mechanism-free) ornithopters do not need conventional motors and mechanisms, potentially saving weight and energy consumption, reducing mechanical complexity, and improving wing flexibility. In solid-state ornithopters, wing flapping can be achieved by surface-mounted piezoelectric actuators. The design of a solid-state ornithopter is a complex multi-disciplinary task, and optimization of wing topology, actuator placement, and excitation parameters requires a computationally efficient model to predict its dynamic response and performance metrics. In this paper, effectively, a novel flight simulation model is presented based on a reduced-order lumped parameter multi-body model coupled with a vortex lattice program. The proposed lumped parameter model can be represented by an equivalent multi-body mechanical model or a circuit model. The coupling considered in the lumped parameter model includes: (1) the body-wing momentum interaction, (2) bend–twist​ coupling of the piezocomposite wings, (3) fluid–structure interactions between the flapping wings, oscillating body, and the ambient fluid, and (4) electromechanical coupling between a resistive–inductive–capacitive driving circuit and the piezocomposite wings. The wing motion is described using the Rayleigh–Ritz method, in which the representative wing modes are identified as spanwise plunge, chordwise curvature, and twist. The body-wing interaction is modeled using Hamilton’s principle. The fluid-induced effects on the wings have three contributions: added mass and damping, quasi-steady aerodynamic forces obtained using the vortex lattice program, and unsteady aerodynamic forces calculated using the Theodorsen formulation, which is integrated into the wing heave and pitch degrees of freedom in the lumped parameter model. The proposed reduced-order model proposed is computationally efficient, suitable for trade studies and multi-disciplinary design optimization, and can be easily converted to state representation for controller development purposes. The capabilities of this model are demonstrated through tethered and gliding flight simulations. System properties such as circuit parameters, structural parameters, excitation frequency ratio, etc., are investigated. Phugoid and short period modes are observed in gliding flight simulations. The contribution of active flapping is found by the comparison of flight simulations with and without active flapping. A net thrust contributed by unsteady lift is demonstrated even though the thrust-lift ratio is low. The proposed model serves as an extensible framework for modeling and design optimization of ornithopters.

Tailored twist morphing achieved using graded bend–twist metamaterials

This work develops a morphing concept that utilises a metamaterial as the passive morphing device for helicopter blades. The metamaterials are created with bend–twist coupling, which enable the blade twist under prescribed bending loads. Finite element analysis (FEA) is performed to investigate the influence of the unit cell configurations on the coupling properties of the metamaterials. The numerical models are then validated experimentally through a set of bending tests conducted with additively manufactured prototypes. Finally, the validated model is used to design a graded metamaterial, where the cell aspect ratio gradually changes along the blade span, providing unique bend–twist coupling and allowing for tailored twist to be obtained. The results suggest the graded metamaterials are capable of introducing optimised nonlinear twists to the blade during different flight conditions including both hover and forward flight.

Influence of Bending-Twisting Coupling Deformation on Pure Bending Strength and Fracture Morphology of CFRP Angle-Ply Laminate

The purpose of this study is to investigate the effect of bending-twisting coupling deformation on the bending strength of CFRP in which laminate configuration has symmetricity and angled fiber orientation. In this study, a novel type of test fixture for pure bending test that permit the coupled bending-twisting deformation is newly developed. Test results showed that the pure bending strength of the angle-ply laminates was decreased when bending-twisting coupled deformation was permitted. The normalized bending strength when the bending-twisting coupled deformation is permitted was decreased with increase of coupled component of angle-ply laminate. Observations of fracture morphology of specimen also showed that the specimen was firstly failure at the 0° layer on the compression side, no matter if the coupled deformation was permitted or constrained. However, when the coupled deformation was permitted, the failure was occurred at lower applied bending stress compared with when coupled deformation was constrained. Moreover, when the coupled deformation was permitted, the failure of 0° layer was occurred at the diagonal portion of specimen. These results suggested that the existing of in-plane shear stress at 0° layer affects the fracture morphology of specimen.

Improving the extension–twist coupling performance of practically warpage-free laminates via layup hybridization

This article investigates whether the extension–twist and bend–twist coupling performance of practically warpage-free laminates can be improved by layup hybridization (carbon/epoxy–glass/epoxy hybrids) compared to non-hybrid (mono) laminates. We performed numerical layup search by simulating the thermal warpage, and the bend–twist and extension–twist behaviour of 4096 4-ply layup permutations. The upper limit of allowable manufacturing-induced warpage was based on the ISO2768 standard. The optimal hybrid and mono layups were selected to have the most significant coupling performance within the allowable warpage range. A mono layup achieved the maximum bend–twist performance (which does not require layup asymmetry), but layup hybridization increased the extension–twist performance by more than 30% in the practically warpage-free range. The numerical results were validated through 3D scanning and 3D digital image correlation–aided mechanical tests. We concluded that layup hybridization can significantly improve the extension–twist performance of realistically usable composite laminates with negligible thermal warpage.

Exploration of the effect of wing component post-buckling on bending-twist coupling for nonlinear wing twist

A new investigated concept for passive load alleviation is to exploit the nonlinear behavior of wing design components to trigger a deformation which reduce loads once a critical load level is reached. The necessary deformation is a torsional rotation which is supposed to reduce the angle of attack. For this target, wingbox sections are investigated regarding their nonlinear behavior with finite element analysis. Parameter studies feature anisotropic carbon fiber reinforced polymer (CFRP) layups for the skins, layups and thicknesses for spars and the presence of stringers. Results show a desired nonlinear progressive bending-torsion coupling for an unstiffened wingbox section, when the upper skin and the rear spar are modified. After modification they are allowed to buckle within the load envelope. The skin has an anisotropic layup. The rear spar needs to be thinner than the front spar. Both modifications result in progressively increasing torsional rotation of the wingbox with increasing load. Stringers are not applied because they limit the nonlinearity which is not desired for the envisioned load alleviation technique.

Analytical and experimental investigation of bend-twist coupling on the vibrational response of multi-layered stepped composite beams

This paper investigates the bend-twist coupling analysis of multi-layered stepped generally orthotropic composite beams subjected to mixed end-of-beam and mid-span supports. Specifically, an analytical closed-form model was developed based on first-order shear deformation theory (FSDT), which discretizes the domain into elements based on the step change of geometry, laminate configuration, or mid-span boundary supports. Hamilton's principle was used to derive the governing equations within each element and connection and boundary equations. The state-Space approach was then utilized to provide an analytical solution. Moreover, an experimental investigation was conducted to validate the mode shapes and natural frequencies of the beam subjected to several mixed boundary conditions. The results are also validated with the literature and a finite element model developed using ANSYS. Comparisons demonstrate the reliability and accuracy of the analytical model.

Optimized blade mass reduction of a 10MW-scale wind turbine via combined application of passive control techniques based on flap-edge and bend-twist coupling effects

In the present work, the possibility of reducing the mass and thereby the capital cost of a 10 MW-scale wind turbine blade is assessed by applying passive load control techniques. Two passive load control methods are combined in the analysis; the bend-twist-coupling method, aiming at reducing operational loads and the flap-edge-coupling method, aiming at alleviating stall induced vibrations in parked or idling operation. The first is materialized through rotation of the composite material plies over the caps of the spar beam, while the second is attained through displacement of the caps in opposite directions. The assessment of the material reduction capacity is performed through optimization simulations. The optimization loop combines an in-house thin lamination tool for the computation of the blade beam properties and the distribution of stresses over the cross sections of the blade and an in-house comprehensive aeroelastic analysis tool that provides the design loads of the turbine. Optimization simulations indicate that an 8.3% reduction in mass can be achieved through moderate modification of the blade inner structure, i.e. concurrent rotation of the plies of the UD material on the caps by 5.8° and displacement in opposite directions of the spar caps by 3% of the chord length.

Model predictive control of wind turbine with aero-elastically tailored blades

The use of aero-elastically tailored blades (ATB) for large wind turbines has shown the benefit of mitigating blade loads, in a passive adaptive manner, with the design of bend-twist coupling (BTC) along the blades. The BTC design makes the blades torsionally flexible and capable of adapting to different wind speeds. However, such increased flexibility makes the turbine modeling computationally demanding and the real-time controller design more challenging. In this work, to include the ATB effect into the turbine model for control, a twofold modeling for ATB characteristics is proposed. First a static BTC distribution is added to the turbine aerodynamics to account for the blade’s pre-bend-twist design, next a second-order transfer function is introduced to approximate the blade structural dynamic response to wind speed variations. The nonlinear model of the whole ATB wind turbine is built up in Simulink, linearized and discretized into a state-space form. A model predictive controller (MPC) is developed with the actuator constraints considered. Simulation studies are conducted on a 5MW ATB wind turbine at a selected above-rated wind speed. The use of the simplified model for control is assessed and the performance of MPC is compared to the gain-scheduling baseline controller.

Multidisciplinary aeroelastic optimization of a 10MW-scale wind turbine rotor targeting to reduced LCoE

In the present paper, multidisciplinary optimization (MDAO) is applied with the aim to reduce the levelized cost of energy (LCoE) of the DTU-10MW Reference Wind Turbine (RWT) rotor. As application paradigm, the widely applied in the literature passive load control method of Bend Twist Coupling (BTC) is considered. The integrated optimization framework combines in a common loop, rotor aerodynamic and full wind turbine structural elasto-dynamic analyses, aiming at determining the optimum rotor diameter, the planform of the blade in terms of twist and chord distributions, the offset ply angle for BTC and the inner structure of the blade with cost function directly the LCoE. It is based on an in-house servo-aero-elastic analysis tool for determining the ultimate loads along the span of the blades and the power yield, whereas a cross-sectional analysis tool is employed for acquiring structural properties of the modified blade and stresses distributions over the blade sections. A cost model of the overall wind turbine is implemented by combining existing in the literature models and open data. The new rotor design is found to have a reduced LCoE by 0.71% and to produce 2.4% higher energy annually due to its increased by 3.7% diameter.

Hierarchical chirality of biofilament induced by its chiral microstructure

Biological filaments with chirality are ubiquitous in biology, but the mechanism behind the chiral growth of these filaments is still unclear. To understand the formation mechanism of these chiral filaments, a hierarchical chiral model for plant tendrils is established in this work based on the Cosserat beam theory and the constitutive equation of chiral materials, which can be used to describe the deformation of chiral biological filaments. Based on this model, the bend–twist coupling chirality is considered, the chirality transfer of plant tendrils from the micro to the macro scale is derived, and the variation in the chirality coefficients with the axial strain is obtained. By introducing a pre-strain and a pre-twist deformation, a theoretical explanation for the swelling and deswelling of plant tendrils is provided as an example. Finally, based on the shooting method, the spatial configuration of plant tendrils under the action of an external force at the end load is obtained. It is found that plant tendrils can achieve regular chiral morphologies or even hierarchical chiral morphologies by adjusting their internal stresses and elastic properties. During this process, the bend–twist coupling is more critical than the stretch–twist coupling. In the presence of external loads, the chiral perversion of plant tendrils can be realized by adjusting the bend–twist coupling coefficient; however, it cannot be realized by adjusting the stretch–twist coupling coefficient. This work is of universal significance and can provide a theoretical guidance for the artificial design and performance optimization of chiral filament materials.

Design optimization and numerical verification of adaptive composite blades for hydro-turbine

In this paper, an adaptive composite blade is designed based on the composite mechanics and bending torsion coupling theory, and the blade structure is optimized by a multi-parameter and multi-objective optimization method. Furthermore, the dynamic interaction between the flow and structure domain during the bend-twist coupling process was also studied by the two-way fluid-structure coupling method to verify the hydrodynamic performance and structural performance of the optimized blade. The results show that the multi-parameter and multi-objective optimization method is suitable for the design of composite blades. The optimized blade has better hydrodynamic performance and structural performance, manifesting a higher energy utilization and less concentrated stress.

A closed-form solution for thermoelastic stress analysis of perforated asymmetric functionally graded nanocomposite plates

Issues related to stress concentration in cracks, perforated plates, and the use of new generation materials to strengthen this type of plates are of great importance. When a functionally graded carbon nanotube-reinforced composite plate (FG-CNTRC) has a hole in its center of the plate that is exposed to a combination of mechanical and thermal loads, due to various couplings such as bending-extension, shear-extension, and bend-twist couplings that occur in the stress–strain relationships and due to the presence of nonhomogeneous equations, the analytical solution approach will be accompanied by new challenges. Hence, a general solution for the FG-CNTRC plates weakened by a central hole is presented. To achieve this goal, the Lekhnitskii complex potential approach is developed using the appropriate conformal mapping function. The present solution provides the ability to calculate the stress distribution of perforated plates made of asymmetric composite laminates and functionally graded materials by introducing holomorphic potential functions in the form of Laurent series. In this research, an attempt has been made to depict the effect of important parameters on the stress resultants and moments around the hole. The results clearly show that the studied parameters significantly change the stress resultants and moments due to thermal and mechanical loads applied to perforated FG-CNTRC plates. As a result, it is possible to significantly reduce stress resultants and moments by properly selecting the values of effective parameters in the design of such perforated plates.

Nonlinear flutter analysis of a bend-twist coupled composite wind turbine blade in time domain

Modern wind turbine blade having large slender structure are vulnerable to aeroelastic instability. Aeroelastic tailoring through bend-twist stiffness coupling is an effective way to improve the aeroelastic performance of such large blades. Effect of geometric nonlinearity is significant in these blades. This study presents a time domain aeroelastic analysis followed by a detailed parametric study of large composite wind turbine blade considering von-Karman nonlinearity in the strain–displacement relationship. Flutter limits of three MW sized namely, NREL 5 MW, SNL 61.5 and SNL 100–00 wind turbine blades considering and without considering geometric nonlinearity are compared. A parametric study of SNL 61.5 is conducted by changing the lamination sequence in the spar cap and all section of blade considering the symmetric and asymmetric skins. It has been observed that both nonlinear and linear structural models i.e., models considering and without considering geometric nonlinearity predict highest flutter speed at the same blade configuration and lamination sequence. However, there is a significant difference in the flutter speeds predicted by these models.

Design of Multi-Coupled Laminates with Extension-Twisting Coupling for Application in Adaptive Structures

The multiple coupling of composite laminates has a unique advantage in improving the macro mechanical properties of composite structures. A total of three hygro-thermally stable multi-coupled laminates with extension-twisting coupling were presented, which were conducive to the formation of passive adaptive structures. Then, the multi-coupled laminates were used to design the bending-twisting coupled box structure, in which the configuration of laminate and box structure could be extended to variable cross-section configuration. The optimal design of stacking sequence was realized, the optimization objectives of which were to maximize bending-twisting coupling of box structure and extension-twisting coupling of laminate, respectively. The effects of multiple coupling on hygro-thermal stability, coupling, failure strength, buckling load, robustness and other comprehensive mechanical properties of laminates and box structures were analyzed by parametric modeling method. The results show that the extension-twisting coupling of laminate and the bending-twisting coupling of box structures can be greatly improved by 450% and 260% at maximum, respectively. Meanwhile, it would have a negative impact on the failure strength and buckling load, which, however, can be minimized by a reasonable paving method. Multi-coupled laminates have good robustness, and the bending-twisting coupling helps improve robustness. Finally, the hygro-thermal stability and mechanical properties were verified by numerical simulation with finite element method.

Analysis of bending-twisting coupling in angle-ply laminates

The purpose of the present study is the evaluation of the bending-twisting coupling effect in the analysis of the DCB test by means of the analytical determination of the energy release rate of angle-ply laminated composites. The aim is to extend a previous work done by the same authors to new laminate configurations. Angle-ply laminates with symmetrical arms are analyzed, since in this case the application of a bending moment by means of the piano hinges causes a torsional rotation in each of the arms. That torsion is prevented by the hinges, due to the configuration of the test. Therefore, there is a non-uniform load distribution applied by the hinges, whose resultant is the applied load P and the resultant moment is an unknown twisting moment mt, which prevents rotation at the point of application. The resolution of the resulting system of forces and moments allows obtaining analytically the energy release rate, and analyzing the terms due exclusively to the bending-twisting coupling.

Parametric study of stress distribution in bimodular curved beam

This paper uses classical beam theory for stress analysis of bimodular material straight and curved beams. Hamilton’s principle is used to obtain the equations of motion. The stiffness parameters are calculated using equivalent stiffness methods to consider various couplings (twisting-stretching, bending-twisting coupling), and the neutral surface position is calculated by the Newton-Raphson method. Through the thickness, normal stress distributions are presented for different stacking sequences, the radius of curvature, and bimodularity ratio for simply supported boundary conditions. It is observed that, unlike unimodular materials, stress distribution for bimodular materials is different in positive and negative side bending. The parametric study showed that the increment of bimodularity ratio increases the magnitude of stress in the tensile zone but decreases in the compressive zone. The effects of couplings are more in angle-ply compared to mixed-ply and cross-ply laminates.